Packet 7 dimensionality reduction

This is an exploration of dimensionality reduction on Packet 7 (last updated: 2019-05-19). KW thought of this in response to the general question of how (if at all) we can distinguish porosity “beliefs” from spiritual “experiences.”

The basic question here is whether we can distinguish beliefs from experience by tracking patterns of covariance across individual participants: What are the “clusters” of questions that tended to hang together at the participant level (i.e., if someone endorsed one question, what else did they endorse)? If porosity and spiritual experience are fully redundant with each other, we would not expect to see separate clusters of porosity vs. spiritual experience items.

Main take-away: If we retain more than 2-3 factors, we end up distinguishing between porosity and spiritual experience. Two standard methods of determining how many factors to retain (parallel analysis and minimizing BIC) both suggest retaining six or more factors.

Exploratory factor analysis (EFA)

Parallel analysis

Parallel analysis suggests retaining 13 factors.

the condition has length > 1 and only the first element will be usedJoining, by = "capacity"
Joining, by = "factor"
Joining, by = "factor"

factor	abs	dse	exsen	hthk	mm	por	se	unev	wob
MR1	.	13	.	.	.	3	11	.	.
MR2	32	.	.	.	.	.	.	.	.
MR3	2	.	.	.	.	.	.	.	6
MR4	.	.	.	.	14	3	.	.	.
MR5	.	.	.	.	.	.	11	.	.
MR6	.	.	.	.	.	.	.	.	6
MR7	.	1	.	9	.	.	.	.	.
MR8	.	.	.	.	.	.	.	6	.
MR9	.	.	.	9	.	.	.	.	.
MR10	.	.	.	.	3	.	.	.	.
MR11	.	.	.	.	.	10	.	.	.
MR12	.	.	7	.	.	.	.	.	.
MR13	.	.	.	.	.	.	.	.	.

Quick interpretations:

• MR1 = spiritual experience I (dse/se)
• MR2 = absorption
• MR3 = other personality (wob/abs)
• MR4 = martha mary
• MR5 = spiritual experience II (se)
• MR6 = sense of control (wob)
• MR7 = need for cognition I (hthk)
• MR8 = launay-slade (unev)
• MR9 = need for cognition II (hthk)
• MR10 = other porosity
• MR11 = porosity
• MR12 = sheep-goat (exsen)
• [MR13 = NULL]

Focus on items that from DSE, SE, Porosity, & MM scales:

Joining, by = c("question", "factor", "scale")
Joining, by = c("question", "scale")

Minimizing BIC

Minimizing BIC suggests retaining 6 factors.

the condition has length > 1 and only the first element will be usedJoining, by = "capacity"
Joining, by = "factor"
Joining, by = "factor"

factor	abs	dse	exsen	hthk	mm	por	se	unev	wob
MR1	.	14	.	.	.	1	10	.	.
MR2	2	.	.	6	.	.	.	.	6
MR3	32	.	4	4	.	.	.	1	.
MR4	.	.	3	.	17	15	.	.	.
MR5	.	.	.	.	.	.	12	5	.
MR6	.	.	.	8	.	.	.	.	6

Quick interpretations:

• MR1 = spiritual experience I (dse/se)
• MR2 = other personality (hthk/wob/abs)
• MR3 = absorption (plus some exsen/hthk/unev)
• MR4 = porosity (mm/por)
• MR5 = spiritual experience II (se/unev)
• MR6 = control (hthk/wob)

Focus on items that from DSE, SE, Porosity, & MM scales:

Joining, by = c("question", "factor", "scale")
Joining, by = c("question", "scale")

Joining, by = c("question", "factor", "scale")
Joining, by = c("question", "scale")

Weisman et al. (2017) retention criteria

The retention criteria employed in Weisman et al. (2017) suggest retaining 2 factors.

the condition has length > 1 and only the first element will be usedJoining, by = "capacity"
Joining, by = "factor"
Joining, by = "factor"

factor	abs	dse	exsen	hthk	mm	por	se	unev	wob
MR1	2	13	4	8	17	16	19	.	5
MR2	32	1	3	10	.	.	3	6	7

Quick interpretations:

• MR1 = porosity + spiritual experience? (“spiritual”?)
• MR2 = absorption + personality? (“secular”?)

Focus on items that from DSE, SE, Porosity, & MM scales:

Joining, by = c("question", "factor", "scale")
Joining, by = c("question", "scale")

Three-factor solution

Just for the hell of it, here’s a three-factor solution.

the condition has length > 1 and only the first element will be usedJoining, by = "capacity"
Joining, by = "factor"
Joining, by = "factor"

factor	abs	dse	exsen	hthk	mm	por	se	unev	wob
MR1	1	13	2	6	14	16	19	.	2
MR2	33	.	4	3	2	.	3	6	.
MR3	.	1	1	9	1	.	.	.	10

Quick interpretations:

• MR1 = porosity + spiritual experience
• MR2 = absorption (+ secular experience?)
• MR3 = controls

Focus on items that from DSE, SE, Porosity, & MM scales:

Joining, by = c("question", "factor", "scale")
Joining, by = c("question", "scale")

Four-factor solution

Just for the hell of it, here’s a four-factor solution.

the condition has length > 1 and only the first element will be usedJoining, by = "capacity"
Joining, by = "factor"
Joining, by = "factor"

factor	abs	dse	exsen	hthk	mm	por	se	unev	wob
MR1	.	14	.	1	.	.	19	.	.
MR2	33	.	6	4	.	.	3	6	.
MR3	1	.	.	7	.	.	.	.	9
MR4	.	.	1	6	17	16	.	.	3

Quick interpretations:

• MR1 = spiritual experience
• MR2 = absorption (+ secular experience?)
• MR3 = controls
• MR4 = porosity (+ personality?)

Focus on items that from DSE, SE, Porosity, & MM scales:

Joining, by = c("question", "factor", "scale")
Joining, by = c("question", "scale")

EXTRA SCRAPS (including only DSE, SE, Porosity, & MM items)